Table of Contents
Preface vii
1 Introduction 1
1.1 General Remarks 3
2 Mathematical Topics 5
2.1 Summary of Necessary Mathematical Formulae 5
2.1.1 Some Basic Group Theory 9
2.1.2 Operators and Eigenvalue Business 10
2.1.3 Differential Vector Calculus 11
2.1.4 Integral Vector Calculus 11
2.1.5 Functions, Distributions, and All Things Fourier 13
2.2 Coordinate Systems and Transformations 15
2.3 Physical Constants and Useful Numbers 18
3 Maxwell's Equations Part I 21
3.1 The Law of Coulomb - Electric Charge, Force, and Basic Measurement 21
3.2 The Law of Gauss - The Electric Field and Some Basic Math 29
3.3 The "Magnetic" Law or the Law with No Name 35
3.4 Voltage and Capacitance 38
3.5 Summary 42
4 Maxwell's Equations Part II 45
4.1 The Conservation of Charge 45
4.2 Electric Currents and the Law of Ampère 50
4.2.1 The Magnetic Flux Density and Current Coupling 52
4.3 The Law of Faraday 55
4.4 The Displacement Current 61
4.5 Summary 67
5 Physical Degrees of Freedom 69
5.1 The Wave Equation and Solutions 69
5.2 Basic Wave Solutions - Scalar Field Theory 72
5.2.1 Solutions in Spherical Coordinates 76
5.2.2 Solutions in Cylindrical Coordinates 79
5.2.3 Comments 80
5.3 Degrees of Freedom - Polarization 81
5.3.1 Polarization in Cartesian Coordinates 81
5.3.2 Polarization in Spherical Coordinates - TE and TM Modes 84
5.4 Gauge Invariance and Potentials 85
5.5 Summary 92
6 Physical Observables 95
6.1 The RLC Circuit 96
6.2 Field Energy, Momentum, and Angular Momentum 100
6.2.1 The Stress Tensor and Conservation of Momentum 101
6.2.2 The Poynting Vector and Energy Conservation 104
6.2.3 Conservation of Angular Momentum 107
6.3 Polarization (Again) Courtesy of Stokes 109
6.4 Summary 113
7 Distributions of Charge, Macroscopic Matter, and Boundary Conditions 115
7.1 Multipoles 116
7.1.1 Interlude on Electric and Magnetic Dipoles 125
7.2 Boundary Conditions 128
7.3 Electromagnetic Interactions with Matter 131
7.4 Electrical Conductivity 135
7.5 Field Equations with General Matter 137
7.6 Summary 139
8 Conclusions and Omissions 141
Exercises and Solutions 143
Bibliography 165
Index 167
